Question

If the fringe width is $0.4mm$, the distance between the fifth bright and third dark band on the same side is

• A. $1mm$
• B. $2mm$
• C. $3mm$
• D. $4mm$

Answer 1

The correct option is A

$1mm$

Step 1: Given

Fringe width, $\beta =0.4mm$

Step 2: Determine the value of $x_5$

The position of the nth bright fringe from central maxima s given by $x_n=\frac{n\lambda D}{d}$

For the fifth bright fringe, $$\begin{gathered} x_5=\frac{5\lambda D}{d} \\ =5\beta -\left(1\right) \end{gathered}$$

($\beta =\frac{\lambda D}{d}$)

Step 3: Determine the value of $x_{3\text{'}}$

The position of the n'th dark fringe from central maxima s given by $x_{n\text{'}}=\frac{(2n\text{'}-1)\lambda D}{2d}$

For the third dark fringe, $$\begin{gathered} x_{3\text{'}}=\frac{\left(2\right(3)-1)\lambda D}{2d} \\ =\frac{5}{2}\frac{\lambda D}{d} \\ =\frac{5}{2}\beta -\left(2\right) \end{gathered}$$

Step 4: Solve the equations

Subtracting equation (2) from (1),

$$\begin{gathered} x_5-x_{3\text{'}}=5\beta -\frac{5}{2}\beta \\ =2.5\beta \\ =2.5(0.4mm) \\ =1mm \end{gathered}$$

Therefore, option A is the correct option.